Problem: Solve for $z$, $ \dfrac{3z - 9}{3z - 8} = 9$
Explanation: Multiply both sides of the equation by $3z - 8$ $ 3z - 9 = 9(3z - 8) $ $3z - 9 = 27z - 72$ $-9 = 24z - 72$ $63 = 24z$ $24z = 63$ $z = \dfrac{63}{24}$ Simplify. $z = \dfrac{21}{8}$